MA 4020: Linear Algebra

All the updates related to MA 4020 are announced here.

### Class timings:

Monday: 2:30 pm to 04:00 pm

Friday: 4:00 pm to 05:30 pm

### Examination and Grades:

The grades will be decided by the marks obtained in the assignments, mid-term, surprise tests, the final examination, and also by the performance in the class.

## Syllabus:

System of Linear Equations, Elementary Operations, Row-Reduced Echelon Matrices, Gaussian Elimination. Vector Spaces, Subspaces, Direct Sums, Bases and Dimension, Linear Maps, Rank-
Nullity Theorem, The Matrix of a Linear Map, Invertibility. Eigenvalues and Eigenvectors, Invariant Subspaces, Upper-Triangular Matrices, Diagonal Matrices.

Inner Products, Norms, Orthonormal Bases, Gram-Schmidt process, Schur's theorem, Orthogonal Projections and Minimization Problems, Linear Functionals and Adjoints.
Self-Adjoint and Normal Operators, The Spectral Theorem for finite dimensional operators. Generalized Eigenvectors, The Characteristic Theorem, The Minimal Polynomial, Jordan Form.
Polynomial, Cayley-Hamilton Theorem, The Minimal Polynomial, Jordan Form.
## References:

- K. Hoffman and R. Kunze, Linear Algebra, PHI Learning, Second Edition, 2009.
- A. Ramachandra Rao, P. Bhimasankaram, Linear Algebra, TRIM Series, 2000.

## Assignments:

The assignments have to be submitted right after the class on the respective due dates. The assignments can be submitted after the due date and time as well,
but only 50% of the marks will be credited into your account, unless you have a valid reason for the late submission. Assignments have to be submitted in A4 white sheets.
- Assignment 1: Updated on: 25.08.2016, Due on 05.09.2016.
- Assignment 2: Updated on: 05.09.2016, Due on 16.09.2016.
- Assignment 3: Updated on: 27.10.2016, Due on 14.11.2016.

Some of the assignments and tutorial sheets are being prepared by Ms. Geethika Sebastian, a tutorial assistant for MA 4020 in July - Nov 2016.